"""
For doctests run following command:
python -m doctest -v counting_sort.py
or
python3 -m doctest -v counting_sort.py
"""

def counting_sort(arr):
    """
    Counting_sort
    Sorting a array which has no element greater than k
    Creating a new temp_arr,where temp_arr[i] contain the number of
    element less than or equal to i in the arr
    Then placing the number i into a correct position in the result_arr
    return the result_arr
    Complexity: 0(n)

    Examples:
    >>> counting_sort([0, 5, 3, 2, 2])
    [0, 2, 2, 3, 5]
    
    >>> counting_sort([-2, -5, -45])
    [-45, -5, -2]
    """

    m = min(arr)
    # in case there are negative elements, change the array to all positive element
    different = 0
    if m < 0:
        # save the change, so that we can convert the array back to all positive number
        different = -m
        for i in range(len(arr)):
            arr[i] += -m
    k = max(arr)
    temp_arr = [0] * (k + 1)
    for i in range(0, len(arr)):
        temp_arr[arr[i]] = temp_arr[arr[i]] + 1
    # temp_array[i] contain the times the number i appear in arr

    for i in range(1, k + 1):
        temp_arr[i] = temp_arr[i] + temp_arr[i - 1]
    # temp_array[i] contain the number of element less than or equal i in arr

    result_arr = [0] * len(arr)
    # creating a result_arr an put the element in a correct positon
    for i in range(len(arr) - 1, -1, -1):
        result_arr[temp_arr[arr[i]] - 1] = arr[i] - different
        temp_arr[arr[i]] = temp_arr[arr[i]] - 1

    return result_arr


if __name__ == "__main__":
    positive_array = [1, 2, 3, 4, 9, 1, 2, 8, 3, 5, 7, 0, 9, 8, 1, 7, 4, 5]
    negative_array = [-5, -6, -2, -3, -4, -5, 0, -9, -2, -3, -8, -4]
    x = counting_sort(positive_array)
    y = counting_sort(negative_array)
    print(x)
    print(y)
